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MEMORANDA ON THE MAYA CALENDA] 
USED IN THE BOOKS OF 
CHILAN BALAM 



BY 



CHARLES P. BOWDITCH 



(From the American Anthropologist (n. s.), Vol. 3, January-March, 1901) 



NEW YORK 

G. P. PUTNAM'S SONS 
1901 



,j:y Tl ■. 






J 



MEMORANDA ON THE MAYA CALENDARS USED IN 
( THE BOOKS OF CHILAN BALAM 

1 By CHARLES P. BOWDITCH 

\ Dr Brinton, in his Maya Chronicles, has translated the follow- 

ing passages from the Book of Chilan Balam of Mani : 

. . . in the .thirteenth Ahau Ahpula died ; for six years the 
count of the thirteenth Ahau will not be ended ; the count of the year 
was toward the East, the month Pop began with (the day) fourth Kan ; 
the eighteenth day of the month Zip (that is) 9 Ymix, was the day on 
which Ahpula died ; and that the count may be known in numbers and 
years, it was the year 1536. 

And again from the Book of Chilan Balam of Tizimin : 

The thirteenth Ahau ; the death of Ahpulha took place ; it was 
the sixth year when ended the count of the; thirteenth Ahau, — the 
count of the year was from the east (the month) Pop passed on the 
fourth Kan ; on the eighteenth of (the month) Zip, 9 Imix was the day 
Ahpulha died ; it was the year 1536. 

In his remarks on these books Dr Brinton says : 

According to the reckoning as it now stands, six complete great 
cycles were counted, and parts of two others, so that the native at the 
time of the Conquest would have had eight great cycles to distinguish 
apart. 

I have not found any clear explanation how this was accom- 
plished. We do not even know what name was given to this great 
cycle,^ nor whether the calendar was sufficiently perfected to prevent 
confusion in dates in the remote past. 

It would seem, however, as if the reckoning of time as given 
in these books is very accurate, fixing a date which would not be 

' It should be noted that the grand cycle, which Dr Brinton refers to, is the period 
of 13 X 7200 days = 93,600 days or 260 periods of 360 days ; while the grand cycle 
according to Goodman's method is 13 x 144,000 days or 5200 periods of 360 days. 

AM. ANTH. N. S. 3 — 9. ,__ 



130 AMERICAN ANTHROPOLOGIST [n. s., 3, 1901 

duplicated within a limit of thirty-five hundred or four thousand 
years. 

The Books of Chilan Balam number the katuns on a different 
principle from that used on the inscriptions or in the Dresden 
Codex, but the two methods can be readily and usefully brought 
together, as the katun itself remains the same in both methods. 
In the inscriptions the katuns are numbered from o to 19, using 
Goodman's method though not his exact nomenclature, and 
twenty of them equal one cycle. In the Chilan Balam books, the 
katuns are named as Katun 13 Ahau, Katun 11 Ahau, etc., these 
being the days with which they begin or with which the previous 
katun ended ; and as after thirteen katuns the same name is again 
given, this nomenclature fixes a date within a period which equals 
13 multiplied by the number of days in a katun. There has been 
a difference of opinion as to this number of days in a katun, but 
it is clear from the Books of Chilan Balam that their reckoning 
was by terms of 20 x 360 days. The followers of Perez, however, 
insist that the length of the katun was 24 x 365 days. Sr Perez 
has indeed made this assertion,' but he rests his opinion to a great 
degree on the fact that the naming of the katuns proceeded in 
the following order, taking their names from the day Ahau with 
which they began, viz. : 

Katun 13 Ahau, 
Katun II Ahau, 
Katun 9 Ahau, 
Katun 7 Ahau, etc., 

and that by starting with a katun which begins with 13 Ahau and 
counting forward a period of 24 x 365 days, we should reach 
another katun beginning with 11 Ahau. But the same result is 
brought about by considering the katun as a period of 20 x 360 
days, as has been shown by Dr Seler, among others ; and since 
the Books of Chilan Balam state distinctly that they reckon by so 



^ Stephens, Incidents of Travel in Yzicatan, p. 441 et seq. 



bowditch] memoranda ON THE MAYA CALENDARS I3I 

many scores of so-called years, and as the initial dates of the in- 
scriptions all reckon in the same way, it is now generally consid- 
ered that the katun consisted of 20 x 360 or 7200 days. An 
objection to considering a katun as 20 x 360 days may be raised 
in that the Books of Chilan Balam use the word " afio " or year, 
but this can be easily explained by the fact that the Spanish 
" year " was the period which most nearly agreed with their tun 
or 360-day period, and that the Books did not pretend to speak 
with scientific accuracy. 

Besides the above count, it is well known that the Mayas had 
a year-and-month count. This consisted in naming each one of 
the twenty days and in attaching to each of these days one of the 
numbers i to 13. Besides this, each day so numbered was declared 
to be a given day of a given month and to occur in a year marked 
by one of the year bearers — as for instance in the Book of Chilan 
Balam, already quoted, where the day is given as 9 Ymix 18 Zip 
in the year 4 Kan, Now this day and this year could recur only 
after the lapse of fifty-two years or 18,980 days. 

It should be noted here that in the inscriptions and in the 
Dresden Codex, the day Ymix was always the day 4, 9, 14, or 19 
of any month, showing that the day i of the month was Eznab, 
Akbal, Lamat, or Ben ; while in Landa and the Books of Chilan 
Balam the day Ymix was the day 3, 8, 13, or 18, showing that the 
day I of the month was Cauac, Kan, Muluc, or Ix. That is^ 
the months in modern times began with the day which followed the 
day with which the months began in more ancient times. As the 
tables are calculated for the inscriptions, it will be well, in order 
to facilitate our calculations, to call the day on which Ahpula died 
the nineteenth of the month Zip, instead of the eighteenth of 
that month. 

Given that the katun consisted of 7200 days, a Katun 13 Ahau 
could not recur until after the lapse of 13 x 7200 or 93,600 days, 
and the recurrence of any day marked by the year-and-month 
count, and occupying any particular place in a given katun, could 



132 AMERICAN ANTHROPOLOGIST [n. s., 3, 1901 

not occur until after the lapse of a period which is found by 
finding the least common multiple of the two numbers 93,600 
and 18,980. This is 6,832,800 days, which is a period of 360 
calendar rounds of 18,980 days or of 52 years each. This is equal 
to 18,720 years, and, in the method of reckoning shown in the 
initial dates of the inscriptions, would equal 3 grand cycles, 
8 cycles, and 9 katuns, or, to use the method of Goodman, 
3.8.9.0.0.0. 

I have said that a day marked by the year-and-month count, 
and occupying any particular place in a given katun, could not 
recur until the lapse of this long period. This would be true if 
the day was specified as being a given day in a given tun in a 
given katun, or even if the day was stated as falling in a given 
uinal of a given tun in a given katun. But in the case before us 
the death of Ahpula is said to have taken place in the Katun 13 
Ahau when six tuns or years of that katun remained unexpired. 
Even with this rather loose designation such a day would not 
recur within a period of 3500 or 4000 years. 

The day 4 Ahau 8 Cumhu seems to have been regarded as 
the beginning day of the beginning cycle of some grand cycle. 
From this day all the initial series of the inscriptions of Copan 
and Quirigua, of Piedras Negras and Tikal, so far as we know 
them, count, except one where this day 4 Ahau 8 Cumhu is itself 
given. In this place (on Stela C of Quirigua) 4 Ahau 8 Cumhu is 
reckoned thus: "Grand cycle glyph .13.0.0.0.0.", while in the 
Temple of the Cross it is declared to be a thirteenth cycle. 
As this was the beginning date, there is reason to believe that the 
beginning cycle of a great cycle received the number 13. 

I give here the first and last terms of a list of the beginning 
days of the Katuns 13 Ahau in a complete round of 18,720 years 
occurring after the beginning of the grand cycle called by Good- 
man Grand Cycle 54, which began with 4 Ahau 8 Cumhu. It is 
of little consequence what particular number is given to the 
grand cycle, as the whole series forms a continuous count, and I 



bowditch] memoranda ON THE MAYA CALENDARS 



133 



shall therefore follow Goodman, who gives the number 54 to the 
grand cycle glyphs common to Copan, Quirigua, etc. 

If 54.13.0.0.0.0. or the beginning of the grand cycle, called 
Grand Cycle 54 by Goodman, begins with 4 Ahau 8 Cumhu, a Ka- 
tun 13 Ahau will appear two katuns after this or with the count of 

54.13.2.0.0.0. 13 Ahau 8 Mol Year 10 Ix, 

and other Katuns 13 Ahau will follow at intervals of 13 katuns as 
here given : 



54.13. 15. 0.0.0. 


13 Ahau 8 Pax 


Year 


6 Ix. 


I. 8. 


3 Xul 




3 Cauac. 


2. I. 


3 Kankin 




12 " 


57.5.19.0.0.0. 


13 Ahau 18 Ceh . 




ri Kan. 


6.12 


13 Uo 




8 Muluc. 


7- 5- 


13 Yax 




4 " 


18. 


13 Cumhu 




13 " 


57. 8. II. 0.0.0. 


13 Ahau 8 Mol 




10 Ix. 



But we are seeking a Katun 13 Ahau in which 14 tuns have 
elapsed and of which 6 tuns still remain unexpired. We must, 
therefore, add 14 tuns or 14 x 360 days = 5040 days to each of 
the dates given and we shall then have the following complete 
list of the beginning days of Tun 14 of Katun 13 Ahau for the 
term of 18,720 years: 



54.13. 2.14.0.0. 


9 Ahau 


18 Zotz 


II Kan. 


15- 




18 Ceh 


7 Kan. 


I. 8. 




13 Uo 


4 Muluc. 


2. I. 




13 Yax 


13 Muluc. 


H- 




13 Cumhu 


9 Muluc. 


3- 7- 




8 Mol 


6 Ix. 


4. 0. 




8 Pax 


2 Ix. 


13- 




3 Xul 


12 Cauac. 


5. 6. 




3 Kankin 


8 Cauac. 


19. 




18 Zip 


5 Kan. 


6.12. 




18 Zac 


I Kan. 


7- 5- 




13 Pop 


II Muluc. 



134 



AMERICAN ANTHROPOLOGIST 



[n. s., 3, 1901 







i«. 




54- 


8. 


II.] 


[4.0.0. 




9- 


4. 
17. 






10. 


10. 






II. 


3. 
16. 






12. 


9- 




55- 


13. 


2.14.0.0. 






IS- 






I. 


8. 






2. 


I. 

14. 






3- 


7- 






4. 


0. 
13- 






5- 


6. 






5- 


19. 






6. 


12. 






7- 


5- 
18. 






8. 


II. 






9- 


4. 
17- 






10. 


10. 






11. 


03. 
16. 






12. 


9. 




56 


•i3. 


, 2. 
15- 


14.0.0. 




I. 


, 8. 






2, 


, I. 
14. 






3 


• 7- 






4 


. 0. 
13. 






5 


. 6. 






5 


.ig. 






6 


.12. 


' 



13 Chen 
13 Kayab 

8 Yaxkin 

8 Muan 

3 Tzec 

3 Mac 
18 Uo 
18 Yax 
18 Cumhu 

13 Mol 
13 Pax 

8 Xul 

8 Kankin 

3 Zotz 

3 Ceh 
18 Pop 
18 Chen 
18 Kayab 
13 Yaxkin 
13 Muan 

8 Tzec 

8 Mac 

3 Zip 

3 Zac 

3 Uayeb 
18 Mol 
18 Pax 
13 Xul 
13 Kankin 

8 Zotz 

8 Ceh 

3U0 

3 Yax 

3 Cumhu 
18 Yaxkin 
18 Muan 
13 Tzec 
13 Mac 

8 Zip 



7 Muluc. 

3 Muluc. 
13 Ix. 

9 Ix. 

6 Cauac. 

2 Cauac. 

12 Kan. 

8 Kan. 

4 Kan. 

1 Muluc. 

10 Muluc. 

7 Ix. 

3 Ix. 

13 Cauac. 
• 9 Cauac. 

6 Kan. 

2 Kan. 

11 Kan. 

8 Muluc. 

4 Muluc. 

1 Ix. 

10 Ix. 

7 Cauac. 

3 Cauac. 

12 Cauac. 

9 Kan. 

5 Kan. 

2 Muluc. 

11 Muluc. 

8 Ix. 

4 Ix. 

1 Cauac. 
10 Cauac. 

6 Cauac. 

3 Kan. 

12 Kan. 

9 Muluc. 

5 Muluc. 

2 Ix. 



bowditch] memoranda ON THE MA YA CALENDARS 



135 



7- 5- 
18. 

8.11. 

9. 4- 

17- 
10.10. 
11.03. 

16. 
12. g. 
57.13. 2.14.0.0. 

15- 

1. 8. 

2. I. 
14. 

3- 7. 

4. o. 

4.13- 

5. 6. 

5-I9- 
6.12. 

7- 5- 

18. 

8.11. 



8 Zac 

3 Pop 

3 Chen 

3 Kayab 
18 Xul 
18 Kankin 
13 Zotz 
13 Ceh 

8U0 

8 Yax 

8 Cumhu 

3 Mol 

3 Pax 
18 Tzec 

18 Mac 

13 Zip 

13 Zac 
8 Pop 
8 Chen 
8 Kayab 
3 Yaxkin 
3 Muan 

18 Zotz 



11 Ix. 

8 Cauac. 
4 Cauac. 

13 Cauac. 

10 Kan. 

6 Kan. 

3 Muluc. 

12 Muluc. 

9 Ix. 
Six. 
I Ix. 

11 Cauac. 

7 Cauac. 

4 Kan. 

13 Kan. 

10 Muluc. 
6 Muluc. 
3 Ix. 

12 Ix. 

8 Ix. 

5 Cauac. 
I Cauac. 

11 Kan. 



The only places where a year 4 Kan appears are at the dates 

55.13. 2.14.0.0.* 9 Ahau 18 Cumhu Year 4 Kan, and 

57. 2.14.14.0.0. 9 Ahau 18 Tzec Year 4 Kan. 

But as the words used are that 6 years (or tuns) remained before 
the end of the katun, and as a slightly longer time than just 6 
tuns may have remained, and as the month Zip in which the 
death of Ahpula occurred is the third month of the year and so 
is near the beginning of the year 4 Kan, it is quite possible that 
the beginning of the Tun 14 may have been in the latter part of 



' It is necessary to remember that, by Goodman's methods, these figures represent 
periods of past time. Thus the number 2 of the katun means that 2 katuns have 
passed, and that the current katun is what we should call the third ; and that o.o 
means that a full count of uinals and kins has occurred and that the current uinal 
and kin are what we should call the first. 



136 AMERICAN ANTHROPOLOGIST [n. s., 3, igoi 

the preceding year; in which case, in addition to the preceding 
dates, the following date might be the one which we are seeking: 

55. 9. 1 7. 14.0.0. 9 Ahau 3 Zac Year 3 Cauac. 

As 9 Ymix 19 Zip is said to be in the year 4 Kan, we shall find 
this date before the dates of the beginning of Tun 14 in the first 
two cases and after the beginning of Tun 14 in the last case. 
This date of 9 Ymix 19 Zip will then be numbered thus, placing 
the three dates in consecutive order : 

i) 55-I3- 2.13. 3. I. 6 tuns 299 days to end of Katun 13 Ahau. 

2) 55- 9-i7-i4.11. I. 5 139 

3) 57. 2.14.13.16. I. 6 39 

In no one of the cases is the date 9 Ymix 19 Zip exactly 6 tuns 
before the end of the Katun 13 Ahau, but it is possible that the 
annalist took no account of fractions of tuns, either in excess of 
the 6 tuns or otherwise. Thus in the first and last cases of 
the three, as first given, he may have said to himself, " There are 
but 6 whole tuns remaining of the katun and I will call it 6," or 
in the second case he may have said : " There are 5 tuns remaining 
and 139 days besides ; I will call it 6 tuns." Whichever was the 
plan he followed, we can have at present no means of ascertaining 
except from the results which we obtain by calculation. 

The date found on Stela 9 of Copan, which is the earliest date 
of these stelae of that place, in which the numbers preceding the 
period glyphs are given by the line-and-dot method, is 54.9.6.10.0.0. 
This precedes the above dates by the following periods : 

i) 0.3.16.3. 3.1. = 548,341 days = 1,502 years iii days. 

2) 1.0.11.4.11.1 = 1,952,861 " = 5,350 " 14 

3) 2.6. 8.3.16.1 =4,667,001 " =12,786 " III " 

If, now, we accept the first date of 55. 13. 2. 13. 3.1. as the date of 
Ahpula's death, we shall have the date of Stela 9 of Copan as 
A.D. 34, since the death occurred in 1536. If we accept the second 



bowditch] memoranda ON THE MAYA CALENDARS 137 

date, 55.9.17.14.11.1., as the true one, Stela 9 must represent a 
date of B.C. 3814, and in the case of the third date, 57.2. 14.13. 16.1. 
in which the period to elapse to the end of Katun 13 Ahau is the 
nearest to an exact 6 tuns, we should throw back Copan to 
B.C. 1 1,250. It is not probable, however, that either of the last two 
dates is correct, both because of the immense time which would 
have elapsed and because the monuments show signs of no such 
age. We are therefore left to the date A.D. 34 as the probable 
date of the earliest stela of Copan which we know of at present. 

The following table gives the earliest and latest dates in Copan 
and Quirigua as far as we know them, together with the dates of 
our calendar corresponding thereto, on the supposition that the 
above date is rightly deciphered : 

Copan : Stela 9, 9. 6.10.0.0 a.d. 34. 

" N, 9. 16. 10. 0.0 = 197 years later than a.d. 34 a.d. 231. 

Quirigua : " C, 9. i. 0.0.0 = 108 -j- " earlier " " say B.C. 75. 

"■ K, 9.18.15.0.0 = 241 + " later " " a.d. 275. 

If this is correct, Copan lasted, so far as the erection of stelae 
is concerned, for about 200 years, and Quirigua for about 3 50 years, 
though of course this may be only a small part of the period of 
their existence. 

The above calculations have been made on the supposition 
that the initial dates record the date of the erection of the stelae, 
and on the further supposition, as has been stated, that the same 
principle of calculating time has been continued from the earliest 
ages. There is, however, some evidence that a change has been 
made, at least in detail. It has already been seen that the begin- 
ning day of the month has been shifted from the Eznab, Akbal 
series to the Cauac, Kan series of days. What difference this 
would have made in the relation of the year-and-month count 
with the long count it is impossible to say without knowing the 
means used to effect the change ; but it is quite likely that this 
relation was not affected. In the Book of Chilan Balam of Mani 



<{[^J^ 



138 AMERICAN ANTHROPOLOGIST [n. s., 3, 1901 

is the entry : " The Thirteenth Ahau ; then Pop was counted in 
order." And in the Book of Chilan Balam of Chumayel we find, 
" The Thirteenth Ahau ; Pop was set in order." This statement 
occurs in the early part of the chronicle, and the calculation of 
the Ahaus goes on after it in exactly the same way as before 
it. This setting in order of Pop would not then seem to have 
made any difference in the long count. At least it is very prob- 
able that it means merely that the seasons and the calendar were 
made to agree. 

Dr Brinton {Maya Chronicles, p. 85) also gives a translation of 
a part of the Codice Perez, which refers to the " Doubling of the 
Katuns." The statement is very obscure, but only tends to 
show that while the counting of the katuns was carried on as 
in the Books of Chilan Balam, the first of the series was called 
Katun 8 Ahau instead of Katun 13 Ahau, while the last of the 
series was Katun 10 Ahau. This would not necessarily change 
the consecutive order of the katuns, but might merely give a new 
starting-point. 

While, therefore, it is impossible to say what change, if any, 
was made in the reckoning of time, it may be said that there 
is no evidence at present to show that the old relation of the long 
count to the year-and-month count and to the count of the Books 
of Chilan Balam did not continue to the time of the arrival of 
the Spaniards. Moreover, the date of A.D. 34 for the monuments 
of Copan and Quirigua is by no means unlikely to be the true 
one. At all events the above discussion of the reckoning will 
not be useless if it succeeds in bringing out new facts, and no one 
will be more ready to recognize any new evidence than I shall be, 
even if the above deductions shall be shown to be erroneous. 



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